Generalization and Completeness of Stochastic Local Search Algorithms
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912835887431680 |
|---|---|
| author | Loscos, Daniel Marti-Oliet, Narciso Rodriguez, Ismael |
| author_facet | Loscos, Daniel Marti-Oliet, Narciso Rodriguez, Ismael |
| contents | We generalize Stochastic Local Search (SLS) heuristics into a unique formal model. This model has two key components: a common structure designed to be as large as possible and a parametric structure intended to be as small as possible. Each heuristic is obtained by instantiating the parametric part in a different way. Particular instances for Genetic Algorithms (GA), Ant Colony Optimization (ACO), and Particle Swarm Optimization (PSO) are presented. Then, we use our model to prove the Turing-completeness of SLS algorithms in general. The proof uses our framework to construct a GA able to simulate any Turing machine. This Turing-completeness implies that determining any non-trivial property concerning the relationship between the inputs and the computed outputs is undecidable for GA and, by extension, for the general set of SLS methods (although not necessarily for each particular method). Similar proofs are more informally presented for PSO and ACO. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14212 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalization and Completeness of Stochastic Local Search Algorithms Loscos, Daniel Marti-Oliet, Narciso Rodriguez, Ismael Neural and Evolutionary Computing Computation and Language We generalize Stochastic Local Search (SLS) heuristics into a unique formal model. This model has two key components: a common structure designed to be as large as possible and a parametric structure intended to be as small as possible. Each heuristic is obtained by instantiating the parametric part in a different way. Particular instances for Genetic Algorithms (GA), Ant Colony Optimization (ACO), and Particle Swarm Optimization (PSO) are presented. Then, we use our model to prove the Turing-completeness of SLS algorithms in general. The proof uses our framework to construct a GA able to simulate any Turing machine. This Turing-completeness implies that determining any non-trivial property concerning the relationship between the inputs and the computed outputs is undecidable for GA and, by extension, for the general set of SLS methods (although not necessarily for each particular method). Similar proofs are more informally presented for PSO and ACO. |
| title | Generalization and Completeness of Stochastic Local Search Algorithms |
| topic | Neural and Evolutionary Computing Computation and Language |
| url | https://arxiv.org/abs/2601.14212 |